The run-time monitoring of web service compositions has been widely acknowledged as a significant and challenging problem. In this paper, we propose a novel solution to the problem of monitoring web services implemented in BPEL. We devise an architecture that clearly separates the business logic of a web service from its monitoring functionality. The architecture supports both "instance monitors" that deal with the execution of a single instance of BPEL process, as well as "class monitors" that report aggregated information about all the instances of a BPEL process. We also define a language for the specification of instance and class monitors. The language allows for specifying boolean, statistic, and time-related properties. Finally, we devise a technique for the automatic translation of all these kinds of monitors to Java programs.